
    \hjD                        S SK Jr  S SKJrJr  S SKJr  S SKJrJ	r	  S SK
Jr  S SKJr  S SKJrJr  S SKJr  S S	KJr  S S
KJrJr  S SKJr  S SKJrJrJrJrJr  S SK J!r!  S SK"J#r#  S SKJ$r$J%r%J&r&J'r'J(r(J)r)  S SKJ*r*J+r+J,r,J-r-  S SK.J/r/  \!" S5      r0\0Rc                  \#\#5      S 5       r2\0Rc                  \#\5      S 5       r2\0Rc                  \%\$5      S 5       r2\0Rc                  \%\%5      S 5       r2\0Rc                  \\%5      S 5       r2\0Rc                  \\5      S 5       r2\0Rc                  \$\&5      S 5       r2\0Rc                  \'\5      S 5       r2\0Rc                  \'\%5      S 5       r2\0Rc                  \'\'5      S 5       r2\0Rc                  \'\$5      S 5       r2\0Rc                  \'\)5      S 5       r2\0Rc                  \(\5      S 5       r2\0Rc                  \-\-5      S  5       r2\0Rc                  \\5      S! 5       r2\0Rc                  \*\5      S" 5       r2\0Rc                  \+\5      S# 5       r2\0Rc                  \\5      S$ 5       r2\0Rc                  \\5      S% 5       r2\0Rc                  \\5      S& 5       r2\0Rc                  \$\)5      S' 5       r2\0Rc                  \%\)5      S( 5       r2\0Rc                  \)\&5      S) 5       r2S* r3\0Rc                  \$\5      S+ 5       r2\0Rc                  \%\5      S, 5       r2g-).    )_aresame)Lambdaexpand_complex)Mul)ilcmFloat)Eq)S)Dummysymbols)ordered)sign)floorceiling)ComplexRegion)	FiniteSetIntersectionIntervalSetUnion)
Dispatcher)ConditionSet)IntegersNaturalsRealsRangeImageSet	Rationals)EmptySetUniversalSetimageset
ProductSet)numerintersection_setsc                     g N abs     X/var/www/auris/envauris/lib/python3.13/site-packages/sympy/sets/handlers/intersection.py_r,              c                 l    [        U R                  U R                  [        U R                  U5      5      $ r&   )r   sym	conditionr   base_setr(   s     r+   r,   r,      s$    q{{LQ,GHHr.   c                     U $ r&   r'   r(   s     r+   r,   r,           Hr.   c                 0    U [         R                  L a  U $ U$ r&   )r
   r   r(   s     r+   r,   r,   $   s    QZZ1&Q&r.   c                     [        X5      $ r&   )r$   r(   s     r+   r,   r,   (       Q""r.   c           	         UR                   (       Ga(  U R                  (       d:  UR                  (       d)  [        [        U R                  UR                  5      5      $ U R                  (       a  UR                  (       a  U R
                  U R                  p2UR
                  UR                  pT[        X$5      n[        X55      nS[        R                  -  U;   a  [        R                  U;   d+  S[        R                  -  U;   a)  [        R                  U;   a  [        U[        S5      5      n[        Xg-  SS9$ UR                  [        R                  5      (       Ga  / n[        S[        SS9n	U R                  (       dg  U R                    HD  n
[        R                  U
R"                  S   ;   d  M&  UR%                  U
R"                  S   5        MF     [        U6 n[        X5      $ U R                  (       a  U R                    H  n
[        R                  U
R"                  S   ;   a  UR%                  U
R"                  S   5        [        R                  U
R"                  S   ;   a2  UR%                  ['        [)        X* 5      U
R"                  S   5      5        [        R                  U
R"                  S   ;   d  M  UR%                  [        S5      5        M     [        U6 n[        X5      $ g g )N   r   T)polarx)clsreal   )is_ComplexRegionr:   r   r   sets
a_interval
b_intervalr
   PiZeror   r   	is_subsetr   r   r   psetsargsappendr   r   )selfotherr1theta1r2theta2new_r_intervalnew_theta_intervalnew_intervalr;   elements              r+   r,   r,   ,   s   

U[[ dii!DEE ZZEKK$//))5+;+;)"1N!-f!= 1446!aff&6!$$& QVVv%5%*+=+4Q<&9" !B&*, , qwwCU. zz::66W\\!_, ''Q8 & !,/L44 ZZ::66W\\!_, ''Q8447<<?* ''2Q(PQ66W\\!_, ''	!5 & !,/L44   r.   c                     U $ r&   r'   r(   s     r+   r,   r,   [   r4   r.   c                    [        S U R                  UR                  S S -    5       5      (       d  g U R                  S:X  a  [        R                  $ [        [        UR                  U R                  5      5      nX!;  a  US-  n[        [        UR                  U R                  5      5      nX1;  a  US-  n[        U [        X#S-   5      5      $ )Nc              3   8   #    U  H  oR                   v   M     g 7fr&   	is_number.0is     r+   	<genexpr>_.<locals>.<genexpr>b   s     8$7q{{$7   r9   r   r>   )allrG   sizer
   r   r   maxinfr   minsupr$   r   )r)   r*   startends       r+   r,   r,   _   s     8AFFQVVBQZ$7888 	vv{zz Cquu%&E~

AEE155!
"C
|qQe1W 566r.   c                 ^    [        U [        UR                  [        R                  5      5      $ r&   )r$   r   ra   r
   Infinityr(   s     r+   r,   r,   s   s    Q

 ;<<r.   c           	      d  ^ [        S X4 5       5      (       d  g U(       d  [        R                  $ U (       d  [        R                  $ UR                  U R                  :  a  [        R                  $ UR                  U R                  :  a  [        R                  $ U nUR
                  R                  (       a  UR                  nUnUR
                  R                  (       a  UR                  nUR
                  R                  (       a  U$ UR
                  R                  (       a  U $ SSKJ	n  S nU" U" U[        S5      5      U" U[        S5      5      -
  5      u  pgUS L =(       a    US L nU(       a  [        R                  $ UR                  5       S   n	U" X)5      n
U4S jn[        [        UR                  UR                  5      5      mU" X*5      nUc  [        R                  $ U" X:5      nUc  [        R                  $ U4S jnU" X5      nU" X5      n[        UR                  5      S:  a  UR                  n[        UR                  5      S:  a  UR                  n[!        UR
                  UR
                  5      n[#        UR$                  UR$                  5      n['        UUT5      $ )	Nc              3   Z   #    U  H!  n[        S  UR                   5       5      v   M#     g7f)c              3   8   #    U  H  oR                   v   M     g 7fr&   rV   )rY   vs     r+   r[   _.<locals>.<genexpr>.<genexpr>z   s     /1;;r]   N)r^   rG   )rY   rs     r+   r[   r\   z   s"     @As////s   )+r   )diop_linearc                 8    U R                   XR                  -  -   $ r&   )rd   step)rm   rZ   s     r+   <lambda>_.<locals>.<lambda>   s    agg&&(r.   r)   r*   c                   > XR                   :X  a  U$ [        U R                   U-
  5      T-  n[        XR                   U-   U5      S   nX0R                   :X  a  O&[        U R                  5      [        U5      :w  a  X2-  nX0;  a  g U$ )N)rd   r   r   rp   )rK   csts1rp   s       r+   _first_finite_point_.<locals>._first_finite_point   s{    =H "((Q,$
 1hhmR(,>
 BGG}R(<	r.   c                    > [        U R                  5      T-  nU R                  R                  (       a  [	        XR
                  U5      nU$ [	        U R                  X-   U5      nU$ r&   )r   rp   rd   	is_finiter   stop)rm   firstrv   rvrp   s       r+   _updated_range_.<locals>._updated_range   sT    !&&\$77uffb)B 	 qww
B/B	r.   )r^   r
   r   rc   ra   rd   is_infinitereversed%sympy.solvers.diophantine.diophantinern   r   as_coeff_Addabsr   rp   r   r`   rb   r|   r   )r)   r*   rK   rM   rn   eqvavbno_solutiona0ru   rx   rw   s2r   rd   r|   rp   s                    @r+   r,   r,   w   s    @!@@@ zzzzuuquu}zzuuquu}zz 
B	xx[[	
B	xx[[ 
xx	xxA 
)B
 Bc
+bU3Z.@@AFB *+tKzz 
	1	B
2
A0 tBGGRWW%&D	R	#B	zzz	R	#B	zzz 
	B		B BGG}q[[BGG}q[[ "((#Erww Dd##r.   c                     U $ r&   r'   r(   s     r+   r,   r,      r4   r.   c                     U $ r&   r'   r(   s     r+   r,   r,      r4   r.   c                   ^$^%^& SSK Jn  [        U R                  R                  5      S:  d.  U R                  R
                  U R                  R                  :w  a  g U R                  S   nU[        R                  L Ga  S n[        U[        5      (       ak  UR                  [        R                  4:X  aL  UR                  R                  nUR                  R                  S   n[        S5      nUR                  XV5      nOU[        R                  L a  [        S5      =pdUGb  U R                  R                  m$U R                  R                  S   m% [        U" T$U-
  T%W4SS95      n[        U5      S:X  a  [        R"                  $ [%        S U 5       5      (       ay  [        U5      S:X  ai  US   u  pUR&                  u  n
T$R                  T%UR                  U
T%5      5      R)                  5       n[+        [-        T%U5      [        R                  5      $ g [/        U$U%4S jU 5       6 $ U[        R0                  :X  Ga;  SS	KJnJm&  U&4S
 jnU R                  R                  nU R                  R                  S   m%[        T%R8                  SS9nUR                  T%U5      nUR;                  5       u  nn[=        U5      nUR                  UT%5      nUR                  UT%5      nUR&                  n[-        T%U5      nUR>                  (       a  OOUR>                  SL a  [        R"                  $ UT%1:w  a  g X=" [@        RB                  " [E        U5      5      T%5      -  nX=" U" U5      T%5      -  n[+        UU5      $ [        U[F        5      (       GaR  SSK$J%nJ&nJ'n  U R                  R                  nU R                  R                  S   m%Su  nnURP                  URR                  nnURT                  (       a  UnOUnU" XRV                  T%5      u  nnU" XRX                  T%5      u  nn [[        S UU 4 5       5      (       Ga  UT%:X  a  [        U5      S:X  a  UR\                  S   nUT%:X  a  [        U 5      S:X  a  U R\                  S   n[%        S UU4 5       5      (       a  g [        R"                  n![[        S UU4 5       5      (       a*  UU:  a  UUnn[G        UUUU5      n"UR_                  U"5      n!OjURa                  [        R0                  5      (       aF  U" UT%[        R0                  5      n#[        U![        [b        45      (       d  U#R_                  U5      n!Og U![        R"                  L a  [        R"                  $ [        U![d        5      (       a.  U!Rf                  [        Rh                  La  [/        [        U!5      6 n!U!b  [+        [-        T%U5      U!5      $ g g g ! [        [         4 a     g f = f)Nr   )diophantiner>   mT)symspermutec              3   J   #    U  H  o  H  o"R                   v   M     M     g 7fr&   )free_symbols)rY   tuplss      r+   r[   r\      s     Dt!^^t^s   !#c              3   N   >#    U  H  nTR                  TUS    5      v   M     g7f)r   N)subs)rY   r   fnns     r+   r[   r\   )  s#     "CU2771ad#3#3Us   "%)denomssolve_linearc           
         > / nU  HV  nT" USU/5      u  pEXA:X  a  UR                  [        U5      5        M1  UR                  [        U[        US5      5      5        MX     [	        U6 $ )Nr   )rH   r   r   r	   r   )exprsr0   solsrZ   r;   xisr   s         r+   _solution_union_.<locals>._solution_union.  s`     D%aSE28KK	#/KKS"Q( ;<  $<r.   )r=   F)invert_realinvert_complexsolveset)NNc              3   B   #    U  H  n[        U[        5      v   M     g 7fr&   )
isinstancer   rX   s     r+   r[   r\   l  s     :Az!Y''s   c              3   (   #    U  H  oS L v   M
     g 7fr&   r'   rX   s     r+   r[   r\   w  s     9&89&8s   c              3   8   #    U  H  oR                   v   M     g 7fr&   )is_realrX   s     r+   r[   r\   }  s     9&899&8r]   )5sympy.solvers.diophantiner   lenlamda	variables	signature	base_setsr
   r   r   r   exprr   r   list	TypeErrorNotImplementedErrorr   anyr   expandr!   r   r   r   sympy.solvers.solversr   r   nameas_real_imagr   is_zeror   	make_argsr#   r   sympy.solvers.solvesetr   r   r   	left_open
right_openr   ra   rc   r^   rG   	intersectrE   r   r   r_   rg   )'rI   rJ   r   r2   gmvarr   solnssolnsolmtr   r   r   fn_f_reimifreelamr   r   r   new_infnew_sup	new_lopen	new_ropeninverterg1h1g2h2	range_setrQ   	solutionsr   r   r   s'                                       @@@r+   r,   r,      s   5 	DJJ  !A%zz##tzz';';;~~a H 1::eX&&5??qzzm+K!!B++''*Cc
ABajj 3ZA>B

$$Q'A[b1vtLM 5zQzz!DDDDu:?!&qJD,,DQ771dii1o6==?D#F1dOQZZ@@ "CU"CDD>
	  JJOOJJ  #166%VVAr]"BBWWR^WWR^Qm:: ZZ5 ::qc\ eBi(!- -H 	OF1Iq11X&&	E8	$	$	6 	6 JJOOJJ  #%$0@0@9	99"H%H!YY*B!YY*B:"b:::Qwr7a< ggajGQwr7a< ggajG
 9w&8999 

I9w&8999 W$'.WG')YO$..|<	??177++ (Aqww 7I%i(L1IJJ$-$7$7$>	AJJ&zz!Iu--)..

2R%tI7	$q!i88u 
%O 23  s   W% %W87W8c                     [        UR                  5      [        U R                  5      :w  a  [        R                  $ [	        S [        U R                  UR                  5       5       6 $ )Nc              3   H   #    U  H  u  pUR                  U5      v   M     g 7fr&   )r   )rY   rZ   js      r+   r[   r\     s     G3F41A3Fs    ")r   rG   r
   r   r"   zipr@   r(   s     r+   r,   r,     sD    
166{c!&&k!zzG3qvvqvv3FGHHr.   c                    [         R                  [         R                  4nU [        U6 :X  aE  U R                  U R
                  pCUR                  (       d  X2;   d  UR                  (       d  XB;   a  U$ U R                  U5      (       d  g SnU R                  UR                  ::  Ga<  UR                  U R                  ::  Ga!  U R                  UR                  :  a  UR                  nUR                  nGOPU R                  UR                  :  a  U R                  nU R                  nGOU R                  n[        U R                  UR                  5      (       d  UR                  R                  [        5      (       a1  U R                  R                  [        5      (       d  UR                  nOwU R                  R                  [        5      (       a1  UR                  R                  [        5      (       d  U R                  nO"[        [        X/5      5      S   R                  nU R                  =(       d    UR                  nU R                  UR                  :  a  U R                  nU R                   n	GOPU R                  UR                  :  a  UR                  nUR                   n	GOU R                  n[        U R                  UR                  5      (       d  UR                  R                  [        5      (       a1  U R                  R                  [        5      (       d  UR                  nOwU R                  R                  [        5      (       a1  UR                  R                  [        5      (       d  U R                  nO"[        [        X/5      5      S   R                  nU R                   =(       d    UR                   n	X-
  S:X  a  U(       d  U	(       a  SnOSnU(       a  [         R"                  $ [        WWWW	5      $ )NFr   T)r
   NegativeInfinityrg   r   leftrightr   _is_comparablerd   re   r   r   hasr   r   r   r   r   )
r)   r*   inftylrm   emptyrd   r   re   r   s
             r+   r,   r,     s    

*EHevvqww199
aii1:H AEww!%%AGGquu,77QWWGGEIWWqwwGGEIGGEAGGQWW-- 77;;u%%aggkk%.@.@GGEWW[[''E0B0BGGE
 !!0399E2q{{I55155=%%CJUUQUU]%%CJ %%CAEE155))5599U##AEEIIe,<,<%%CUUYYu%%aeeii.>.>%%Cwu~.q155C5J;!jEzzE3	:66r.   c                 "    [         R                  $ r&   )r
   r   r(   s     r+   r,   r,     s    ::r.   c                     U$ r&   r'   r(   s     r+   r,   r,     r4   r.   c                 @    [        U R                  UR                  -  6 $ r&   )r   	_elementsr(   s     r+   r,   r,     s    q{{Q[[022r.   c                 n     [        U  Vs/ s H  o"U;   d  M
  UPM     sn6 $ s  snf ! [         a     g f = fr&   )r   r   )r)   r*   els      r+   r,   r,     s:    5"1W25665 s   	' 	""' ' 
44c                     g r&   r'   r(   s     r+   r,   r,     r-   r.   c                     U $ r&   r'   r(   s     r+   r,   r,     r4   r.   c                     U $ r&   r'   r(   s     r+   r,   r,     r4   r.   c                     U $ r&   r'   r(   s     r+   r,   r,     r4   r.   c                 D    UR                   [        R                  L a  UR                  [        R                  L a  U $ [        [        U R                  [        UR                  5      5      [        UR                  5      S-   5      n[        X!5      $ ! [         a     g f = f)Nr>   )_infr
   r   _suprg   r   r`   ra   r   r   r   r   r$   
ValueError)r)   r*   r   s      r+   _intlike_intervalr     sv    66Q'''AFFajj,@H#aeeWQVV_-uQWW~/AB && s   ;B AB 
BBc                     [        X5      $ r&   r   r(   s     r+   r,   r,     r7   r.   c                     [        X5      $ r&   r   r(   s     r+   r,   r,     r7   r.   N)4sympy.core.basicr   sympy.core.functionr   r   sympy.core.mulr   sympy.core.numbersr   r   sympy.core.relationalr	   sympy.core.singletonr
   sympy.core.symbolr   r   sympy.core.sortingr   $sympy.functions.elementary.complexesr   #sympy.functions.elementary.integersr   r   sympy.sets.fancysetsr   sympy.sets.setsr   r   r   r   r   sympy.multipledispatchr   sympy.sets.conditionsetr   r   r   r   r   r   r   r   r    r!   r"   sympy.simplify.radsimpr#   r$   registerr,   r   r'   r.   r+   <module>r     s   % 6  * $ " . & 5 > . K K - 0  H H ( 23  L,7 8 L#.I /I Hh/ 0 Hh/' 0' Hh/# 0# M3/,5 0,5\ He, - E8,7 -7& E8,= -= E5)o$ *o$d E8, - E9- . Hc*` +`F J
3I 4I Hh/A7 0A7F Hc* + L#. / Iy13 23 Is+ , C% & Hi0 1 Hi0 1 Iu- . Hh/# 0# Hh/# 0#r.   